migration

clojure/examples/1_2_functions.clj

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+(chapter "Custom Functions")
+
+(section "Simple Functions")
+(example "Define function"
+         (defn square [x] (* x x)))(example "Use function"
+         (square 8))
+(example "Multi-arg functions"
+         (defn mul-add [a b c] (+ (* a b) c))
+         (mul-add 3 10 5))
+(example "Nullary function"
+         (defn nullary [] 10)
+         (nullary))
+(example "Anonymous functions"
+         ((fn [x] (+ x x)) 10)
+         (#(+ % %) 10)
+         (#(+ %1 %2) 10 20))
+(example "Functions as values"
+         (defn twice [f] (fn [a] (f (f a))))
+         ((twice square) 3))
+
+(section "Recursive Functions")
+(example "Recursive Fibonacci"
+         (defn rec-fib [n]
+           (cond
+             (== 0 n) 1
+             (== 1 n) 1
+             :else (+ (rec-fib (- n 1))
+                      (rec-fib (- n 2)))))
+         (rec-fib 40))
+(example "Memoized Fibonacci"
+         (def mem-fib
+           (memoize
+             (fn [n]
+               (cond
+                 (== 0 n) 1
+                 (== 1 n) 1
+                 :else (+ (mem-fib (- n 1)) (mem-fib (- n 2)))))))
+         (mem-fib 90))
+(example "Tail-recursive Fibonacci"
+         (defn iter-fib [n]
+           (letfn [(iter-fib' [n a b]
+                     (if (== 0 n)
+                       a
+                       (iter-fib' (- n 1) b (+' a b))))]
+             (iter-fib' n 1 1)))
+         (iter-fib 90)
+         (iter-fib 10000)
+         (defn iter-fib-recur [n]
+           (letfn [(iter-fib' [n a b]
+                     (if (== 0 n)
+                       a
+                       (recur (- n 1) b (+' a b))))]
+             (iter-fib' n 1 1)))
+         (iter-fib-recur 10000))
+(example "Explicit loop Fibonacci"
+         (defn loop-fib [n]
+           (loop [n n a 1 b 1]
+             (if (== 0 n)
+               a
+               (recur (- n 1) b (+ a b)))))
+         (loop-fib 90))
+
+(section "Pre and Post conditions")
+(example "Fast power"
+         (defn power
+           "Raises a to the b-th power"
+           [a b]
+           {:pre [(<= 0 b)]
+            :post [(or (zero? b) (zero? a) (zero? (rem % a)))]}
+           (cond
+             (zero? b) 1
+             (even? b) (power (* a a) (quot b 2))
+             (odd? b) (* a (power a (dec b))))))
+(example "Pre and postconditions ok"
+         (power 2 5)
+         (power 2 0)
+         (power 0 2))
+(example "Precondition violated"
+         (power 2 -5))
+(example "Invalid postcondition"
+         (defn ipower
+           [a b]
+           {:pre [(<= 0 b)]
+            :post [(zero? (rem % a)) (<= 0 %)]}
+           (power a b)))
+(example "First part of invalid postcondition violated"
+         (ipower 2 0)
+         (power 2 0))
+(example "Second part of invalid postcondition violated"
+         (ipower -2 3)
+         (power -2 3))